Abstract
Abstract Given a principal bundle with a connection, we look for an asymptotic expansion of the holonomy of a loop in terms of its length. This length is defined relative to some Riemannian or sub-Riemannian structure. We are able to give an asymptotic formula that is independent of choice of gauge. We also show how our results from sub-Riemannian geometry can give improved approximations for the case of studying expansions of holonomy of principal bundles over the Euclidean space.
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